One general category of an optical Sagnac rotation sensor is a fiber-optic resonator gyroscope (FORG). The FORG is a high-resolution spectroscopic device employing a single laser for simultaneously determining the clockwise (cw) and counterclockwise (ccw) ring cavity resonances. A highly coherent laser is required to resolve these cavity resonances and their Sagnac shifts. The FORG requires multi-loop control circuits and the output closed-loop signal will be a beat frequency, f.sub.B, where ##EQU1## where: .OMEGA.=the effective inertial rotation rate (including instrument bias) about the sensitive axis rad /s)
A=area enclosed by the optical circuit PA1 L=perimeter of the area enclosed by the optical circuit PA1 .lambda.=wavelength of the light source PA1 n=waveguide index of refraction.
For a circular ring of radius R, equation (1) becomes ##EQU2##
The requirement for a coherent light source in the FORG renders it necessary to eliminate or reduce optical interference and coupling between the oppositely directed traveling wave modes of the ring cavity. Thus, the ring cavity modes should be non-degenerate so that noise spectra and coupling effects will be beyond the bandwidth of the FORG control loop. This non-degeneracy can be accomplished by selecting different longitudinal mode numbers for the cw and ccw waves, e.g., successive modes in the frequency domain. Such a frequency separation is the basis of a two mode FORG in which the cw wave is in the N.sup.th cavity resonance longitudinal mode and the ccw ave is in the N'.sup.th cavity resonance longitudinal mode, where N.noteq.N'. In such a system, however, it is necessary to be able to differentiate between environmentally induced changes in the free spectral range (i.e., mode separation in the frequency domain) and the Sagnac shift indicative of the rotation applied to the fiber optic loop.